The French mathematician Émilie du Châtelet, who had a sound grasp of Newtonian mechanics, developed Leibniz's concept and, combining it with the observations of Willem 's Gravesande, showed that vis viva was dependent on the square of the velocities.

Members of the academic establishment such as John Playfair were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the second law of thermodynamics but in the 18th and 19th centuries, the fate of the lost energy was still unknown. Gradually it came to be suspected that the heat inevitably generated by motion was another form of vis viva. In 1783, Antoine Lavoisier and Pierre-Simon Laplace reviewed the two competing theories of vis viva and caloric theory.[1]Count Rumford's 1798 observations of heat generation during the boring of cannons added more weight to the view that mechanical motion could be converted into heat. Vis viva now started to be known as energy, after the term was first used in that sense by Thomas Young in 1807.

An excerpt from D.Bernoulli's article, published in 1741,[1] with the definition of vis viva with 1/2 multiplier.

The recalibration of vis viva to include the coefficient of a half, namely: